A Method Based on Congestion Game Theory for Determining Electoral Tendencies Guillermo De Ita1 , Luis Altamirano1 , Aurelio L´ opez-L´ opez2 , and Yolanda Moyao1, 1
2
Faculty of Computer Sciences, BUAP, M´exico {deita,altamirano,ymoyao}@cs.buap.mx http://www.cs.buap.mx/ ´ Instituto Nacional de Astrof´ısica, Optica y Electr´ onica
[email protected] http://ccc.inaoep.mx/
Abstract. We present a novel method to study the tendencies of vote in sectorial democratic elections. Our method is intended to determine the relevant profiles characterizing the political behavior of voters. Those profiles allow us to model how the voters, in a specific election organized by sectors, make their vote decision. Furthermore, the same set of profiles are used for representing the different strategies applied by the candidates that compete in the election. We apply congestion games theory to simulate the distribution of the votes among the candidates, describing an automated way to estimate the likely number of votes for each candidate. Therefore, we can determine who will be the winner candidate of the election, according to a specific political scenario. We report the application of our model to simulate the elections of a director in a university setting, obtaining estimations very close to the actual outcomes. Keywords: Social Behavior Modeling, Social Simulation, Electoral Simulation, Congestion Games, Multi-Agent System.
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Introduction
In Artificial Intelligence (AI), the application of intelligent agents has brought a great deal of commercial interest, and it has shown useful for decision making. As more and more commercial transactions are performed on networks, there is a growing interest in designing smart autonomous agents performing specific actions. One of the possible applications of intelligent agents is to simulate specific human tasks. For example, an important human task has been the selection of a representative from a population. The selection of a representative is both an important and common issue in democratic systems, for instance; the candidate of a political party, the head of a
This research was partially supported by PROMEP. The first and third author was in addition partially supported by SNI, M´exico.
K. Aberer et al. (Eds.): SocInfo 2012, LNCS 7710, pp. 162–173, 2012. c Springer-Verlag Berlin Heidelberg 2012
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department, a local city mayor, and so on. This process refers to the need to elect the best representative within a group of people, according to their perception expressed as votes. Different mathematical formalisms have been developed to describe electoral systems and outcomes by modeling both voting rules and human behavior (see e.g. [1, 4, 10–12]). In [5, 11], an analysis on the winning coalition structure of an election system is done as a simple legislative game, considering the importance of relative ideological positions in a legislative decision game, that is, as a noncooperative game. While in [1, 3, 9], the dynamics of their model is based on applying the search for equilibrium points, which must fulfill the expectations of voters and the optimum policy choices of representatives, assuming stationary environments. In [12], they report and effort to account for political attitudes and beliefs in a computational model, which is based on a psychological theory. This model was compared against another previously proposed model based on Bayesian learning. The new model could reproduce more political attitudes when applied on simulations of a presidential campaign in 2000. Nowadays, demoscopic studies (opinion polls) are accomplished in order to determine some electoral preferences. Those surveys, as snapshots of a moment, allow us to make predictions for a very short term. An opinion poll, in its traditional elaboration form, usually reflects outlying questions about the candidates, and about the political competition, such as; popularity indexes, perceptions on the nature of the candidates or their images, the impact of their campaigns, mottos, etc. Often the factors that are measured through those surveys point more to the interest of the candidates or their parties, than to the interest or perception of the voters. Due to this panorama that lacks the necessary analytic tools for studying electoral tendencies, we propose a simulation system of the political behavior for certain voter segments in accordance to the changes of strategies that the candidates perform during their campaign. A key element to find the winner of an election is to recognize the profiles characterizing the voters, given that all agents form their set of strategies based on promises and actions which try to influence the voters. Those promises and actions are reflected via a set of weights assigned to the profiles characterizing the voters. We consider each one of the candidates as an independent player with his own strategies. Each agent competes against each other in order to win a political election, i.e., the political election is a competition among all the players. As the profiles used for characterizing the voters, and forming the strategies of the agents have a limited nature, then a congestion game is formulated. Thus, we can consider our logical model as a formulation of a congestion game [3, 9, 13]. A congestion game consists of a set of players, a set of resources, strategies for each player, and a cost function associated to each resource. A state of the game is defined by the strategies each of the players has selected, where each of the players is assumed to act selfishly, traying to minimize his individual cost. A congestion game can be modelled as a congestion network, i.e. a triple
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(A, P∫ , k), where A is the set of n players, P∫ is the set of limited resources, and k is the increasing cost function which depends on the number of players using the same resource. As mentioned, every player Ai ∈ A has to choose a strategy which allows to decrease its cost function value. A state e = (s1 , . . . , sn ) is reached when each player selects a strategy si . In a congestion network, several players simultaneously aim at allocating sets of resources. The cost of a resource (one edge of this network) is given by a function of the congestion, i.e. the number of agents using the same resource. So, each agent Ai ∈ A chooses a strategy forming a state e = (s1 , . . . , sn ) and the cost function is computed for all limited resource and according to the state e. Building a congestion game for the problem at hand allows us to perform a search for the singular points in the competition system [13], enabling to predict the possible winner of the specific election. In each singular point of the contest, we can determine the winning strategy and the candidate who will obtain the maximum number of sectors, that is, we can determine who will be the winner, as well as the winning strategy. The paper is organized as follows. Section 2 explains how voters are characterized. We discuss a method for determining preferences in profiles of a sector of voter in Section 3. The process of defining the strategies of competitors is detailed in Section 4. In Section 5, we present how to compute the estimation of number of votes for candidates. Finally, Section 6 includes conclusions and further work.
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Characterizing a Population of Voters
Our method starts by considering that there exists a population of voters distributed in k sectors, let P ot = {Z1 , Z2 , . . . , Zk } be the k voter sectors. Let W Zi = |Zi | be the number of voters within the sector Zi . We assume that the cardinalities W Zi , i = 1, , k are known values. Let A = {A1 , A2 , . . . , An } be a set of n intelligent agents. Ai ∈ A represents one of the competitors contending for a position or, in political terms, a candidate competing in an election. A sector Zi , i = 1, . . . , k is favorable to the candidate who obtains the majority of the votes, with respect to the number of votes obtained by the other candidates. We describe herein a novel method to determine the competitor who obtains the maximum number of sectors in a democratic election. A relevant element in our method is to determine the main ”profiles” used for characterizing the political behavior of the members of each sector, as well as to determine its relative political importance among them. Usually, analysts can approximate those profiles and their relative positions, after analyzing previous elections and carrying out a deep study on the political behavior of the voter population. We represent the profiles used to characterize voters via a discrete set P∫ = {P1 , . . . , Pm }. The elements of P∫ are called ”profiles”. Such profiles are the key objects used to characterize how the voters base their vote decisions. The members of each sector are characterized and identified by specific values on the
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set of profiles which represents the main political characteristics of the members in that sector. In our method, the set P∫ is also used to represent the set of strategies applied by the competitors to attract the preferences of the voters. The quantity on a profile that an agent believes to have in certain features (profile entry) is represented by a weight. An agent (and sometimes, his campaign team) organizes the profiles and their corresponding weights in different ways, creating in this manner different political programs to be applied, in accordance with the answer of the population to those programs. We call to each of the agent programs a strategy. An agent applies one of its strategies to compete with other agents in order to obtain a maximum number of sectors of the population. A strategy si of Ai is a set of pairs: si = {(P1 , wi1 ), (P2 , wi2 ), . . . , (Pm , wim )}, where each weight wij , j = 1, . . . , m tries to reflect the importance of the profile Pj that the agent Ai assigns in one of its political programs (si ). In fact, each agent (or his advisers) has to determine which profiles (and their corresponding weights) the agent should promote, and he also has to plan how to arrange those profiles in his political program. According to the different scenarios or to the results obtained through the opinion polls during campaign, as well as to the agent knowledge about the preferences of the voters, the agent selects one of his strategies. Let S(Ai ) = {si1 , si2 , . . . , sini } be the set of different strategies that the agent Ai ∈ A can apply for attracting voters. Once all agents have chosen one of their strategies si ∈ S(Ai ), i = 1, . . . , n, a state (an action now in a multi-agent system) is formed e = (s1 , . . . , sn ) ∈ S(A1 )X . . . XS(An ). Let S = {e1 , . . . , eo } be the set of different states of the multi-agent system. Then, a state ej , j = 1, . . . , o is one of the possible configurations of the multiagent system, and according to the strategies applied by the different agents, they can obtain a certain number of votes in each state. As the agents change their strategies during campaign in order to obtain more votes, they interactively form new states in this multi-agent system. While more and more agents utilize the same limited profile, such profile tends to saturate, and its influence on the voters will also become smaller and smaller. Thus, a congestion game is an ideal formalism for modeling this kind of resource sharing [3, 9]. In our study, we consider how to distribute the votes among the agents in a specific state e ∈ S. Thus, we develop a method to estimate the number of votes obtained by each agent, according to the strategy that each one applies. We applied the method to model the election of the Director of the Faculty of Computer Sciences (FCC) in the State University of Puebla (BUAP), M´exico, realized in March, 2011. During this election, the process was organized in 11 sectors; 5 belonging to faculty members (professors), 5 to students and 1 to administrative workers. We applied the model to recognize the main political preferences of the students when they make their political vote.
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In the FCC, there are two undergraduate programs: Computer Sciences and Computing Engineering. For each program, there are two sectors: Basic and Advanced. Then, there are four sectors at undergrad level; Basic Eng, Advanced Eng, Basic Cs, Advanced Cs, and additionally one sector at graduate level (M. Sc.): Graduate. There are about 1900 students at the undergraduate level and 46 students at graduate level. There are 117 faculty members and 15 administrative workers. In this election, 1448 of undergrad students and 40 graduate students cast their voted. While 100% of administrative workers and 111 professors voted. The political preferences of professors and administrative personnel during the elections in the FCC were captured via classical opinion polls, this due to the size of those sectors. In fact, the largest size of any of those sectors was 32 professors. Then, we could collect, for all professors and administrative personnel, their political preferences. On the other hand, the size of the student population and their vague answers for determining only one preferable candidate, generated the adequate scenario to validate our model. Thus, we simulate the tendencies of the vote just for the five student sectors.
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A Method for Determining a Hierarchy of Preferences on the Student Profiles
An opinion poll was applied to the students in order to assign a relative importance order on the student profiles, according to what they considered from more to less important for making their vote decision [2]. We found that the following twelve features in profiles were the most important for students to consider when they decide their vote: P1 : Opinion of classmates, P2 : Opinion of academic advisers, P3 : Opinion of course instructors, P4 : Opinion of political student groups, P5 : Opinion of official administration, P6 : Commitment shown by the candidate, P7 : Academic background of candidate, P8 : Political group supporting the candidate, P9 : Political work during the campaign, P10 : Possible contact with the candidate, P11 : Image and confidence shown by the candidate, P12 : If the students are in favor of reelection of director in post. Given a sector Zi ∈ P ot, a weight wzij for each profile Pj ∈ P∫ is computed based on responses obtained in an opinion poll. We processed the opinion poll and we computed the average of the responses. Thus, a list of values wzij were obtained as the average of the values assigned to the profile Pj , j = 1, . . . , m by the selected sample of each student sector Zi , i = 1, . . . , k. An adjustment based on minimum squares was applied to the sample in order to eliminate ’false positives’. The false positive cases are represented as responses of voters who do not want to cooperate with the opinion polls, either when they try to be tricky, submit contradictory answers, or have apathetic responses. And such cases are detected when the responses of one poll is quite different to the average of that sector.
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An order of relevance is given on the profiles of each sector Zi ∈ P ot. Let AvPj Zi be the relative value given to the profile Pj with respect to the other profile values of the sector Zi . We want that the values AvPj Zi , j = 1, . . . , m represent relative percentages that determine a relative order on the set of profiles characterizing Zi , and also that the values AvPj Zi build a hierarchy among the profiles of the same sector. In general, there are different methods for determining a hierarchy of preferences among a list of values (see [6–8]). One of the most simple methods for determining an order on the preferences of the individuals is for example, that the values AvPj Zi are taken as the percentages of members from Zi in which the profile Pj is their main profile. Other simple method for determining relative percentages AvPj Zi , is to assign the same importance to all profiles and then, each percentage AvPj Zi is equal to 100% divided by the number of relevant profiles in Zi . In our model, it is important to distinguish between profiles with a positive impact and those which have a negative impact, when the students make their vote decision. In general, the sum of the percentages of the positive profiles is higher than the sum of the percentages of the negative ones, because the positive profiles had a greater influence than the negative ones to decide the vote, in a proportion according to the voting scenario which is being modeled. For example, according to the atmosphere that prevailed during the election in the FCC, we detected that positive profiles had more impact than negative ones. The sum of the percentages on positive profiles was 100%, while the sum of the percentages on the negative profiles generally produced values from 40% to 50%. So we detected that the total positive profiles influence was twice or thrice than the negative profiles influence, according to the student sector. We determine, through an analysis of the responses of the opinion polls, that the first seven more valuable profiles ranked by the students have a positive impact, while we give to the remaining four profiles a negative influence. According to the opinion poll applied to the students, the average values wzij from 1 to 7 were the most significative profiles, 1 being the most relevat profile value. Then, by computing P osij = 11 − wzij we can determine a relative position in the hierarchy of the positive profiles given in ascending order, that is, 4 is the less important and 10 is the most important value on the positive profiles. Given a fixed sector Zi , i = 1, . . . , k, in order to build a relative order among positive profiles of the sector, the values P osij are summed on all positive profiles: Sum P ositivei = P osij and then the relative percentage of a positive profile is defined as: AvPj Zi = P osij /Sum P ositivei . The case of the profile 9; ”P9 : effect of the P olitical Campaign”, was considered at the beginning of the election very conservatively, because we did not know beforehand how intense or effective the campaign of the candidates will be. So a conservative assessment was assigned to P9 with a relative percentage equal to the maximum relative percentage on the other positive profiles. The last values obtained from the responses of the student poll represent negative profiles. The negative profiles have obtained average values wzij between
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8 and 11. We assign a relative order among them, according to the formula: P osij = wzij − 7, since 7 was the turning value between positive and negative profiles. In a similar way as we did for positive profiles, a relative order was computed for the negative ones. First, we add the values P osij on all negative profile: N egativei = P osij . A special profile was P12 specified as: ”Do you agree with the re-election of the director?.” In the opinion poll, P12 shown a very important negative character since a high percentages of the students reject the idea of the re-election of the current director. So, we assigned a relative value on P12 equal to the addition of the position values of all negative profiles previously considered. Then, the relative value for the profile P12 was P osi12 = N egative. Since P12 was dominant in the set of all profiles which have considered negative and has an influence equivalent to the addition of the other negative profiles. Then, we had a total value of the sum of all negative profiles (including P osij on the set of the negative profile 12), defined as: Sum N egativesi = profiles. And for each negative profile, we compute its relative percentages as: AvPj Zi = P osij /Sum N egativesi . Table 1. Matrix M P ot : Relative weights to profiles by sectors Profile Basic Eng Adv Eng Basic Cs P1 -1.1062 -2.789 -2.957 P2 -0.9878 -0.194 9.58 P3 10.896 10.361 10.46 P4 -1.3414 -1476 -1.7 P5 -1.15 -2.0354 -1.73 P6 19.565 19.458 16.64 P7 16.197 17.651 15.96 P8 11.677 12.168 10.91 P9 39.13 38.916 33.278 P10 14.92 14.94 13.563 P11 13.958 13.615 11.364 P12 -38.646 -39.124 -35.463
Adv Cs Graduate -0.9381 -3.06 -0.187 9.51 9.41 8 -2.44 -1.66 -4.41 -1.22 17.47 17.956 15.46 17.07 12.5 11.11 34.95 53.867 15.6 12.889 13.844 12.62 -39.5 -35.31
In Table 1, we present the matrix M P ot containing the final relative percentages AvPj Zi obtained by our ordering method. Negative values are indicators of profiles with a negative impact on the students. Those values show relative percentages among the set of profiles and give a degree of relevance of each profile in the students, when they make their vote decision. Notice that the relevance of each profile is different according to the sector of the student (the five columns of the matrix).
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Defining the Strategies of Competitors
Central information to model democratic elections is based on the political campaigns (strategies) applied by the competitors during the contest.
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In the election that we have modeled, there were two agents competing for the position of director. Of course, the competitors do not know precisely neither the most important profile nor its relevance in the sector. Although, they intuitively recognize the importance of some profiles and they try to influence the voters through their political programs (strategies). The Matrix St shown in Table 2 contains weights representing the final strategies considered during the simulation of the election. The strategies of each candidate can be considered as a vector of twelve values, each value represents the intention of the candidate to influence the voters trough that corresponding profile. Each weight wij ∈ St represents the value on the profile Pi that a competitor determines to apply in its strategy to attract votes. Since the two competitors applied different programs and promises between undergraduate and graduate student sectors, they really used different strategies according to the student academic level (i.e. undergraduate or graduate). The weights constituting the strategies of the candidates were computed based on: their curriculum vitae, the proposals, the political group supporting the candidates, and in this particular case, the knowledge and perception that some of the authors have about both candidates. Table 2. Matrix St : Final Candidates Strategies for Student Level Profile Dir Undergrad Dir Grad Opp Undergrad Opp Grad P1 9.5 5 5 8 P2 8 9.5 5 4 P3 7 9 8 5 P4 8.5 8.5 5 5 P5 6 6 3 3 P6 7 7 4 4 P7 8 8 5 5 P8 8 8 6.8 6.8 P9 6 9 8.5 5.5 P10 7 7 7 7 P11 8 8 6 6 P12 10 10 1 1
For any other election, opinion polls can be designed to calculate the corresponding weights in order to specify in a vector of weights the agent strategies. Each agent applies one of its strategies creating a state e of the multi-agent system. The agents change their strategies according to the opinion polls that they are aware of. For each state e ∈ S, the voters make their vote decision and then every candidate obtains a determined number of votes in concordance with its strategies. In a dynamic way, any candidate could change his strategy with the intention to obtain more votes, forming in this way the different sceneries along the election process.
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Given a state e = (s1 , . . . , sn ) ∈ S, an improvement step for an agent Ai is a change of strategy from si to si going to a new state e and where his percentages of votes increases with respect to the previous value. The neighborhood of a state e consists of those states that derive from e only in one change of the agent strategy [3]. Given the two tables M P ot and St both of m rows (m profiles), and the two different strategies applied by the candidates, one for undergraduate students and the other for graduate students. We show in the following section, how to compute automatically the number of votes expected by each candidate, according with its strategy and the characterization of the sectors.
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Computing the Number of Votes for Each Candidate
For the first four sectors Zi , i = 1, . . . , 4, corresponding to undergraduate student sectors, an addition on their relative percentages multiplied by the corresponding strategy on the set of 12 profiles, of the two candidates is done 12 (w ∗ AvP Z ) and U g = that is, U gi1 = 12 j,1 j i i2 j=1 j=1 (wj,2 ∗ AvPj Zi ), where s1 = (w1,1 , . . . , w12,1 ) is the undergrad strategy applied by the candidate 1, and s2 = (w1,2 , . . . , w12,2 ) is the undergrad strategy applied by the candidate 2. Let StP ri = U gi1 + U gi2 be the total n of the set of profiles to be shared among all agents. In general, StP ri = j=1 U gij expresses the total influence of the profiles on sector Zi to be shared among the candidates. And, according to congestion game theory, the proportional part that a candidate Al ∈ A has to receive when he applies a strategy on the undergraduate sectors is computed as S(e, Al , Zi ) = (U gil /StP ri ) for l = 1, . . . , n and i = 1, . . . , 4. We compute the case for the graduate student sector: Z5 , in a similar way that the case of undergraduate sectors but now we consider the graduate strategies applied by the candidates. Then, if now s1 = (w1,1 , . . . , w12,1 ) is the graduate strategy applied by the first candidate and s2 = (w1,2 , . . . , w12,2 ) is the graduate 12 strategy applied by the second candidate, and so, Grad51 = j=1 (wj,1 ∗AvPj Z5 ) 12 and Grad52 = j=1 (wj,2 ∗ AvPj Z5 ) will be the contribution of the candidates to the graduate sector. Additionally P s5 = Grad51 + Grad52 represents the total of the set of profiles to be shared among all agents. And the proportional part that a candidate Al ∈ A has to receive when he applies his strategy on the graduate sector is: S(e, Al , Z5 ) = (Grad5l /P s5 ) for l = 1, 2. Given that we are considering that the cardinality of each sector W Zi , i = 1, . . . , 5 is known and they are constant values, and although the agents promise more than before (his strategies si , i = 1, . . . , n have higher values), the values W Zi do not change, then a congestion game is modeled to distribute a fixed value of votes among the agents [9]. Then, the cardinalities W Zi , i = 1, . . . , 5 have to be divided proportionally among all agents due to S(e, Al , Zi ). Given a state e ∈ S and for all sectors Zi ∈ P ot, for each agent Al ∈ A, we denote as the percentages of voters from
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the sector Zi which are potential voters for the agent Al , as #Vote(Al , Zi ), and that value is computed as: #V ote(Al , Zi ) = W Zi ∗ (
S(e, Al , Zi ) ) 100
(1)
The value #Vote(Al , Zi ) represents the percentages of members in the sector Zi which are potential voters for Al , l = 1, . . . , n. Then, #Vote(Al , Zi ) has to be computed for all sector Zi ∈ P ot in order to know the percentages of votes that all agent can obtain in each sector. When the election is by sectors, the candidate who obtains a maximum percentages of votes in that sector is the candidate who wins the total sector. Then, fixing a sector Zi ∈ P ot, the candidate who wins Zi is defined as the candidate Aq , q ∈ [1, n] such that: #V ote(Aq , Zi ) = max{#V ote(Al , Zi ), l = 1, . . . , n}
(2)
Notice that given a state e, there is an agent who wins the maximum number of sectors, we call such an agent the candidate in the state e, and is denoted as the competitor Aq , q ∈ [1, n] such that the number of sectors Zi , i = 1, . . . , k that Aq has won is maximum on the set of competitors. Although to change an agent strategy (even if the the candidate in the state e does not change his strategy) represents a change in the state from e to e , and the candidate who wins a maximum number of sectors could change too. The improvement over the number of votes of an agent Ai is necessary to obtain a higher number of sectors for him. Given a state e, a move of improvement for an agent Ai through local values is done by the search of a neighbor e where Ai wins a higher number of sectors than in the state e. In our system, we can analyze the fluctuations of the votes tendencies in order to organize the strategies of a specific agent, either as ’bad’ or ’good’ strategies, according to the number of sectors that the agent wins. Furthermore, we can find which are the best strategies for a particular candidate, according to a specific electoral scenario. Assuming that all people really vote, we have a fixed total number of votes and, if we look for an optimal point, the search could turn cyclic, meaning that if an agent reduces his number of votes, then any other agent will increase his own number of votes. So, some agents could always improve their number of votes from one neighbor to another. An adequate variable to avoid a cyclic search is to consider the percentage of potential voters who abstain in each sector. Although the abstention is a fact in democratic systems, to determine this percentage requires a profound analysis of the traits and behavior of the population in previous elections. In our system, the political campaign is developed during a certain period, in such a way that when a candidate recognizes a new way to improve his strategy, that new strategy is applied and then, the likely number of votes have to be re-computed for all the involved candidates. This continues until no further impact can be produced on the number of votes or when the election campaign is over.
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Fig. 1. Percentages of votes obtained by opponent to incumbent
We analyze the percentages of the votes assigned to each candidate according to the strategies applied by the agents. The formulas presented in this section allow us to estimate the number of votes for each agent, and to know who will be the candidate in the state e according to the current scenario e. Comparing the estimated results at the end of the campaign versus the actual percentages of votes in the modeled election, the absolute errors on the percentages of the votes obtained for the candidate labeled as Opponent to incumbent, were: 2.5, 2.5, 11.5, 3.6, 7.2, which correspond to the sectors: Basic Eng, Basic Cs, Advance Eng, Advance Cs and Graduate (labeled as Postgrade) sectors, respectively, as depicted in Figure 1. If we want to model elections at the scale of, for example, city mayor, the key issue in our proposal is the partition of the voters into sectors (e.g. retired people, workers, government employees, housewifes, etc.) with common and recognized interests and needs (profiles). That implies that we do not only have to know the sizes of the sectors, but we also have to analyze the political and economical historical behavior of those sectors. The demoscopic studies can be helpful for recognizing the profiles and their relative importance among them. Of course, this implies a bigger effort than only applying the common opinion polls for analyzing political preferences. However, more precise predictions request deeper studies and our model can serve as a guide for performing those studies.
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Conclusions
We have designed a model for simulating the process of selecting a representative in a democratic system organized by sectors. Our system can be used to study the tendencies of the vote and for this, it is necessary to determine the relevant profiles that characterize the political behavior of voters. Those profiles model how the voters, in a specific election organized by sectors, make their vote decision.
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In our proposal, we assume that each candidate determines a finite set of strategies (political programs). Each one of these strategies is formulated as a set of weights on the profiles characterizing the voters. The profiles used for characterizing the voters, and for expressing the strategies of the agents, have a limited nature. Consequently, a congestion game is formulated. We present a model to simulate the distribution of the votes among a set of candidates, allowing so, to determine who will be the winner in a specific political scenario. We have applied our model to simulate the elections of a director in a university setting, obtaining estimations very close to the actual outcomes. Future works includes the extension of the model to consider other election scenarios and the application of our model in other electoral process to confirm its validity.
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